One recurring source of debate is the question of how much a playmaker improves his linemates' shooting percentage.

Just asking whether some players repeatedly post high on-ice shooting percentages is not digging deep enough. Every year, the Canucks have an above-average shooting percentage during the minutes that Henrik Sedin is on the ice, but how much of that is because he individually shot for a high percentage, how much is because he played with teammates who are skilled at taking dangerous shots, and how much is because he actually helped his teammates' shooting?

I previously took a semi-quantitative look at this, listing some of the best playmakers in the game and how their various linemates shot with and without them. In this article, we'll revisit that analysis and attempt to work out more precisely how large of an effect there might be.

Henrik Sedin: a shot quality king

Four years' worth of 5-on-5 data were collected, from the 2008-09 season to the 2011-12 season. For any given player, we can collect all of the shots his linemates took when he was on the ice. We can calculate what the expected shooting percentage for that group is (see example calculation below). We know what the actual shooting percentage was, and the difference between the two would be taken as the boost that player provided to his teammates' shooting percentage.

Let's return to Henrik Sedin as an example.

Over this period, he was on the ice for 656 shots by Daniel Sedin, 425 shots by Alexandre Burrows, 173 shots by Alexander Edler, 147 shots by Kevin Bieksa, and so on. Since Daniel Sedin shot 11.9% over this period, we would expect him to have 0.119 * 656 = 78 goals; we would expect Burrows (and his 15.3% shooting) to have 0.153 * 425 = 65 goals, and so forth.

Run through the whole list of everyone Sedin played with over the four-year span and you find that you'd expect to have 217 goals on 2273 shots, which works out to 9.5% shooting. They actually scored 245 goals, on 10.7% shooting, so when playing with Sedin their shooting percentage was bumped up by 1.2%. When you add in Sedin's own shots, that improves the shooting a little more to 299 goals on 2643 shots, 11.3%. The result is the following breakdown of Sedin's on-ice shooting percentage:

League average shooting over this span: 8.2%
Boost from playing with strong linemates: +1.3%
Boost from adding in Sedin's own high shooting percentage: +0.6%
Boost from Sedin's playmaking skills: +1.2%Total: Sedin's on-ice shooting percentage: 11.3%

We can compare those shot quality-related results to his impact on shot totals. The Canucks got 48.9% of the shots with him off the ice and 53.6% of the shots with him on the ice, so his impact on shot differential resulted in an extra 409 shots, or 46 goals, comparable to his individual shooting and impact on teammate shooting combined.

Everyone else

I started with Sedin because his consistently high PDO (shooting percentage plus save percentage) makes him a favorite example for those who argue that shot quality is important. Let's take a look at some of the other leaders in assists over this time period and the per-year impact of various factors:

Player

Expected sh% for his teammates

Quality of teammates impact (goals/year)

Teammates' actual sh%

Playmaking skills impact (goals/year)

H. Sedin

9.6%

+7.5

10.8%

+7.0

Crosby

8.5%

+1.1

10.6%

+8.0

Malkin

9.1%

+3.6

10.3%

+5.5

Backstrom

9.4%

+5.9

10.1%

+3.4

Getzlaf

9.5%

+6.4

9.7%

+1.5

Thornton

8.5%

+1.8

8.7%

+1.4

St. Louis

9.7%

+7.0

10.4%

+3.5

Datsyuk

8.0%

-0.9

9.1%

+5.3

B. Richards

9.5%

+4.5

10.6%

+4.5

Ovechkin

9.1%

+3.7

9.9%

+3.9

Average

9.1%

+4.1

10.0%

+4.5

Top-end playmakers can boost their teammates' shooting percentage by something like 1%, good for an extra 5 goals or so per year. That is certainly significant, although it is clear that neglecting the impact of playing with good shooters can lead to overestimating how significant the shot quality factor is by roughly 2x.

I also wanted to look at some players who were good but not great, so I went to the second page of assist leaders and took the top 10 guys who were with the same team for the whole period (which makes the with-or-without-you analysis easier):

Player

Expected sh% for his teammates

Quality of teammates impact (goals/year)

Teammates' actual sh%

Playmaking skills impact (goals/year)

J. Staal

8.4%

+0.6

8.3%

-0.2

Franzen

8.2%

+0.0

8.6%

+1.5

Hudler

7.6%

-1.8

7.4%

-0.8

Legwand

7.4%

-3.3

7.7%

+1.2

T. Ruutu

8.0%

-0.6

8.8%

+2.9

Backes

8.0%

-1.0

8.5%

+2.3

Dubinsky

8.3%

+0.3

8.7%

+1.7

Hartnell

8.5%

+1.3

9.2%

+3.3

Horcoff

8.0%

-0.5

7.8%

-0.8

Okposo

7.7%

-1.5

7.5%

-0.7

Average

8.0%

-0.7

8.2%

1.0

Now you can see why it is often presumed that on-ice shooting percentages will regress to the mean in the long run. This is not a list of superstars, but they are quality players who averaged nearly 30 assists per 82 games. Yet on average they boosted their teammates' shooting percentage by just 0.2%. Given that the standard deviation on their four-year on-ice shooting percentage is about 0.6%, we can't really identify any of these players as having any real impact on their teammates' shooting percentages.

And this returns us to the reason many statistical analysts focus on shot differential rather than shooting percentages. Four years' worth of data is enough to identify the truly high-end shooting talents, but for the vast majority of players we can wait until the end of their careers and still not know for sure whether a high on-ice shooting percentage reflected anything other than random chance. It is very difficult to look at this list of top-6 forwards' collectively negligible impact on shooting percentage and believe that the Maple Leafs' consistently high shooting percentage with puck-averse Luke Schenn on the ice is due to any particular talent that he possesses.

These ten players see their teams get an extra 2.2% on average of the shots with them on the ice. That works out to about 47 shots per year, or 4.0 goals per year. This second tier of skill players gets four times as much benefit from driving possession as from driving shooting percentage -- nearly as much as the elite players get from driving shooting percentages. And when we go looking for players with possession talent, we can identify a lot more players with a lot more confidence than we can for shooting talent.

For a very small number of elite playmakers, the ability to drive shooting percentage can be a major component of their value. For the vast majority of the league, driving possession is a more significant and more reproducible path to success.

The goals per year thing is a little sloppy, now that I think about it, because it's tied to how many shots were actually taken when the player was on the ice (which is influenced by games played, TOI per game, and tendency to push the puck forwards). I just took the actual shots taken, multiplied by the boost in shooting percentage, and divided by four years.

Crosby boosted his linemates' shooting by 2.1%. The other top playmakers are in the 1% range. It's not unreasonable to say his playmaking skills are double what anyone else in the league does.

When you calculated Daniel Sedin's 11.9% shooting percentage, did that include the time when he played with H. Sedin? If so, you are almost certainly under estimating the impact.

Also, I am not surprised Jordan Staal doesn't look so good because you are comparing Pascal Dupuis's shooting percentage with Staal to his overall shooting percentage (I assume) which includes a lot of ice time with Crosby and Malkin. The fact that Jordan Staal has a negative impact just tells me he isn't as good as Crosby and Malkin at boosting shooting percentage. No surprise there. It doesn't mean he is a 'negative impact' playmaker though.

Considering this it also doesn't surprise me that your second tier of players (essentially second liners) are more or less neutral. First tier players (first liners) have a positive impact, second tier (second liners) are neutral, third tier and below (third and fourth liners) are probably negative.

As @SteveBurtch pointed out on Twitter and David Johnson pointed out here, I used the players' overall shooting percentage instead of their shooting percentage without the playmaker, which underestimates the effect slightly -- otherwise you introduce large errors from players (like DSedin) who had a very small number of shots when apart from the playmaker in question and therefore have very uncertain measures of their shooting talent.

Nevertheless, I've calculated the numbers the other way as well; these are probably more accurate but less precise, so any specific number here might be off, but the overall difference of a couple tenths of a percent between these numbers and the ones above are probably reasonable.

HSedin boosts linemates by 1.9%, good for 12 goals per year (though this number has a large error since it is so highly influenced by DSedin's performance in the small number of shots apart).

Crosby boosts linemates by 2.6%, good for 10 goals per year.

Malkin boosts linemates by 1.5%, good for 2 goals per year.

Backstrom boosts linemates by 1.0%, good for 4 goals per year.

Getzlaf boosts linemates by -0.3%, good for -2 goals per year.

Thornton boosts linemates by 0.6%, good for 4 goals per year.

St Louis boosts linemates by 1.0%, good for 5 goals per year.

Datsyuk boosts linemates by 1.9%, good for 10 goals per year.

B Richards boosts linemates by 1.3%, good for 4 goals per year.

Ovechkin boosts linemates by 0.6%, good for 2 goals per year.

Overall average for the top ten is a 1.2% boost (up from 0.9% in story) and 5 goals per year (up from 4.5). I don't think this changes the conclusions appreciably.

In the minutes that a player is on the ice with one of the very best playmakers in the league, his shooting percentage will be about 1% better. For a player who gets ~150-200 shots per year and plays ~40-60% of his ice time with that top-tier playmaker, that's less than a one-goal boost. It's just not that big of a factor.

As for the argument about second-line players being expected to be a net neutral; the point isn't just that the shooting percentage effect is small for those players -- it's that the effect is swamped by their shot differential, which gets at the heart of why we neglect shooting percentage corrections in most player evaluations. The playmaker correction might be important if you're trying to rank the top ten players in the league, but the vast majority of player signings, trades, and evaluations involve players in the lower 95% of the league, where the shooting percentage factors are small and dominated by variance.

"it's that the effect is swamped by their shot differential, which gets at the heart of why we neglect shooting percentage corrections in most player evaluations."

Some 5v5 stats for the 4 years from 2008-09 to 2011-12.

Average shooting percentage is 7.9%.
Average shots per 60 minutes 5v5 is 29.7.
Max SF/60 while on ice for a forward is 35.9, or 6.2 SF/60 over average (Stalberg).
That equates to an extra 508 shots over 82 60 minute games. At 7.9% shooting percentage that is 40 goals.

29.7 shots per 60 minutes over 82 games is 2435 shots. Increasing shooting percentage by 1.2% equates to an increase of 29 goals.

So, the best players at generating shots (not factoring for zone starts) would generate 40 extra goals using an average shooting percentage (one standard deviation in SF/60 is about 16 goals). And this isn't even taking into account his line mates ability to boost SF totals (i.e. the 40/16 goals can't completely be attributed to the individual).

The best players at increasing their line mates shooting percentage using a mean shot rate would increase goal production by 29 goals.

Tell me again how this is not important? And this is not even taking into account the players ability to increase his own shooting percentage.

Really interesting work, Eric. It might be interesting to look by combination as well as by individual. For example, do players benefit more from playing with both Henrik and Daniel than they do with just Henrik? And if so, is it fair to assign the entire difference in shooting percentage to Henrik as we've done above?

David raised a similar issue in his point about Staal being compared mostly to instances that have either Crosby or Malkin on the ice. The "Without" data in these With-or-Without calculations aren't random, but are instead highly influenced by a few specific players in each case.

It just highlights the complexities of hockey analytics. Accounting for the impact of teammates on individual performance and vice versa is really difficult especially if you want to try to compare players on different teams.

Yeah, that's why I didn't put Daniel in the table; the two of them play together so often that they're basically just one guy as far as the analytics are concerned.

It's true that the without sample is always influenced by the depth of the lineup. Hopefully some of that averages out by looking at a large handful of players from different teams, but just like with Corsi Rel, obviously when you're evaluating an individual player you'd want to make note of who you're comparing against.

What makes you think starting in the offensive zone leads to high-percentage shots?

If anything, given that shooting percentages are very low in shots taken right after a faceoff (see http://www.arcticicehockey.com/2011/12/14/2636414/a-back-door-attempt-at-the-shot-quality-prize or http://forechecker.blogspot.com/2006/10/21st-century-hockey-analysis-begins.html), I would expect offensive zone starts to slightly lower a player's shooting percentage.

But overall, over this four-year span, Henrik Sedin had 612 offensive zone starts above what an average player would have had. Since each offensive zone faceoff nets under 0.4 shots (on goal or missing the net) between the faceoff and the first clear or stoppage (see http://www.broadstreethockey.com/2012/2/2/2752390/philadelphia-flyers-zone-entries), that's something like 7% of the shots that were taken with Sedin on the ice. Those shots would have to average about 25% shooting -- meaning a shot following a faceoff is comparable to a shot at 5-on-3 -- to have even a 1% impact on these numbers.

So I don't buy your hypothesis that "Sedins get easy sheltered zone starts so the higher sh% is expected". The data points the other way, if anything, and the effect is probably negligible in any event.

"We can compare those shot quality-related results to his impact on shot totals. The Canucks got 48.9% of the shots with him off the ice and 53.6% of the shots with him on the ice, so his impact on shot differential resulted in an extra 409 shots, or 46 goals, comparable to his individual shooting and impact on teammate shooting combined."

This comparison to the preceding paragraph is not fair. You compare his effect on shooting percentage v. the goals you would expect his linemates to obtain when shooting without him. But you compare the possession results with the whole rest of the team. In order to be a fair comparison you would actually need to compare the possession results of his linemates while he was not on the ice, with the same zone start ratio correction.

I suspect Sedin didn't have too much ice-time with the scrubs, so the possession numbers when he was off the ice probably sucked worse than his linemates would have faired with him off the ice.

Plus his well known zone start tilt will also have enhanced his possession rate especially in comparison with the guys he was not on the ice with.

It is entirely likely you have well overstated Sedin's effect on possession and scoring here.

You're right -- that's a very good point -- although in this particular instance it doesn't seem to make much difference.

Using David's WOWY page for faceoff-adjusted Corsi (http://stats.hockeyanalysis.com/showplayer.php?pid=602&withagainst=true&season=2008-12&sit=f10&type=corsi) and doing the same sort of weighted-average analysis, I come up with his linemates collectively being 49.2% players.

I'm sure there are some players above for whom the underestimate is larger. But on the other hand, teams mixing their lines up mitigates this effect, and few teams stick with a single combination as much as the Canucks do.